$A$ current $I$ flows through a uniform wire of diameter $d$ when the mean electron drift velocity is $V$. The same current will flow through a wire of diameter $d/2$ made of the same material if the mean drift velocity of the electron is :
Medium
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$j=\frac{I}{A}=n e v_{d}$
$\frac{4 I}{\pi d^{2}}=n e v$
$\frac{161}{\pi d^{2}}=n e v^{\prime}$
From equaiton $( I )$ and $( II )$
$\frac{4 I}{16 I}=\frac{v^{\prime}}{v^{\prime}} \Rightarrow v^{\prime}=4 v$
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